Abstract : In this paper, we test the local isotropy of higher order statistics in the intermediate wake region. We focus on normalized odd moments of the transverse velocity derivatives, M2n+1(partial derivative u/partial derivative z) = \textless((partial derivative u/partial derivative z)(2n+1))over bar\textgreater/\textless((partial derivative u/partial derivative z)(2))over bar\textgreater((2n+ 1)/2) on the wake centreline, which should be zero if local isotropy is satisfied (n is a positive integer). It is found that the relation M2n+1(partial derivative u/partial derivative z) similar to R-lambda(-1) is supported reasonably well by hot-wire data up to the seventh-order (n = 3), although it is also dependent on the initial conditions. In particular, the present data show that the higher the order (e.g. fifth-or seventh-order), the higher R-lambda must be for local isotropy to be satisfied (i.e. M2n+1(partial derivative u/partial derivative z) = 0).